"I'm about to file for 2020"  No you are not about to file for 2020.  In 2020 you will be preparing and filing a 2019 tax return, when the 2019 tax year is over.

You do not say which state you lived in and which you worked in.  You should have prepared the return for the state you did NOT live in first, then the return for the one you lived in.  Is that how you did it?

Check your e-file status for the state returns and see if the other return was accepted:

https://turbotax.intuit.com/tax-tools/efile-status-lookup/

Federal and state refunds come from completely separate entities.  You cannot expect them to arrive at the same time.

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

The way you worded your question also makes me wonder if you mean you lived and worked in NY for part of the year, and then moved to NJ and lived and worked there.  Which was it?  If that was the case, you would have needed part-year returns for each state.

Ok ... to start you just filed your 2018 return and next January (2020)  you will file your 2019 tax return. 

Now did you successfully file the NJ return ? 

Check to make sure your return was accepted:

https://turbotax.intuit.com/tax-tools/efile-status-lookup/  

If it was accepted, then make sure you are using the correct information to track your refund

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund